GROVE CITY, Pa. — As presidential talk steadily grows around him, a fundamental question lingers over Jeb Bush: Does he, as probable rival Chris Christie recently said, have the "fire in the belly to do this?"

Two appearances last week in starkly different settings — a black-tie dinner Monday in Manhattan and a commencement address Saturday at the Christian college that bears this town's name — suggest that the former Florida governor is summoning the energy and exposing his strengths and weaknesses for a 2016 campaign.

"If you feel inspired to serve your fellow citizens, don't let the ugliness of politics keep you from pursuing public office. There's always room for informed, engaged, passionate leaders at every level of government," Bush told the graduates of Grove City College, an hour's drive north of Pittsburgh, imploring them to work hard in whatever they choose.

Speaking on the 60th anniversary of Brown vs. Board of Education, Bush said progress has been made, but "not nearly enough," citing an achievement gap between white students and minorities. He criticized a federal government that is "willingly violating" religious freedom and made the case for immigration reform as an economic engine.

He was relaxed, if a bit rushed in delivery, and mixed in humor about his mother who a year ago quipped that some other family should have a chance at the White House. "Since she's in the advice-giving business these days — I don't know if you've noticed — I asked her what I should speak about today. And she said, 'Jeb, speak about 15 minutes and then sit down.' "

Bush, 61, beat her by more than a minute.

Mark Johnson, an engineer from Ohio whose daughter was among the 585 graduates, said as he listened to Bush, he thought, "I'd vote for this guy." The Republican added, "And I was really turned off by his brother."

Bush remains serious but undecided, according to close friends and advisers, but his conspicuously busy schedule increasingly resembles a pre-campaign, replete with informal outreach to donors and intimate talks with key religious leaders. (He lunched this month at the Biltmore Hotel in Miami with Russell Moore of the Southern Baptist Convention.)

The education policy wonk has widened his message, injecting speeches with more emotion and anecdotes. No one will accuse Bush of having too much charisma, but he's clearly turning it up.

"It looks to me like he's well along to making the decision later this year that he's going to run," said Mel Sembler, a St. Petersburg developer who is a major Republican fundraiser and close to Bush. "He's making appearances in the right places."

Bush is enjoying a surge in interest, in part because of the troubles Gov. Christie faces in New Jersey, having supplanted him as the favorite of the donor class and climbing to the top of polls. Through it all, he is cultivating an image as a big thinker more interested in getting things done than waging the kind of ideological war that has pulled his party to the right — someone eager to avoid the "vortex of a mud fight," as he recently said.

In a sign of his seriousness and organization, talking points were recently distributed to people in Bush's inner circle. The private memo, for use when reporters call, reads: "Of the top considerations he has mentioned, Governor Bush has said he wants to know: He can run a campaign joyfully, and bring optimism to the debate when the nation is increasingly pessimistic about politics and government and uncertain about the future. It's in the best interests of his family."

The memo seeks to tamp down speculation about Bush's hectic schedule and fundraising (he has done it all in the past) and whether he'll base a decision on what other candidates do, calling him a "methodical, thoughtful person."

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Bush's wife, Columba, is profoundly shy and was little-seen in Tallahassee when he was governor from 1999 to 2007. Friends say she will weigh heavily in a decision, but they are quick to point out that other candidates' spouses surely feel similar concern about the rigors and scrutiny a presidential campaign brings.

Already Bush's business dealings have received a fresh look. A front-page story in the New York Times last month cataloged the corporate boards he sits on, including the bankrupt Miami building company InnoVida, as well as $2 million Bush has earned from Tenet Health Care, a major backer of Obamacare. There is no suggestion Bush knew about the InnoVida troubles, and a Tenet executive told the Times that Bush made his objections to the health care law known at board meetings.

But those issues may be secondary to the problems Bush would face with his family name and involvement in a pair of issues that are anathema to the conservative base: immigration and the Common Core State Standards for education.

There's a disconnect between the enthusiasm Bush sees among Republican elites and the sentiment among grass-roots activists. Conservative blogs and forums are full of criticism on a range of fronts.

"If you poke that bear and wave Common Core in front of them, you're going to get a reaction," said Larry Nordvig, executive director of the Richmond (Virginia) Tea Party. "It's the poster child of big government overreach and trying to brainwash the next generation."

Bush appears exasperated by the swelling controversy over Common Core, which has gone beyond conspiracy theories and taken root with frustrated parents across the country, including the states he visited last week.

"I believe high, lofty expectations are a huge part of making sure that children learn," Bush said Monday night at the swanky dinner put on by the Manhattan Institute, a conservative think tank. "And whether they are Common Core State Standards or higher standards in general, we cannot pull back and dilute and dumb down our standards."

He was equally forceful about the need for immigration reform. Bush has enraged some conservatives by saying people who come here illegally may be lawbreakers but most do it for their families — "an act of love."

"For the life of me I have a hard time understanding why people are fearful of our own heritage, our own history," Bush said in New York. "The rules are, you come to this country, you pursue your dreams, you create value for yourself and your families and others, and great things happen to you and to our country. Why would we ignore that at a time when we need to restart and rejuvenate our economy? It makes no sense to me."

Rudy Giuliani, who introduced Bush, talked about how the fluent Spanish speaker was elected with a majority of the Hispanic vote. "Wow," Giuliani said. "It just could be that our party could win an emerging group and get a big vote and change the nature of politics. Oh, well, I hope we can."

"There's a lot of speculation that he may run for president," Giuliani said. "He's got a very, very high problem to overcome: He's got a record of success."

Even among the receptive Wall Street audience there was concern that the Bush name may be an impediment. It was echoed in Pennsylvania and in interviews with voters this month in New Hampshire, where U.S. Sen. Marco Rubio dropped in.

"No more Bush. It isn't that I don't like Jeb. I just don't think he's the man for the time now," said Julie Brown, 79, who attended a speech by Rubio, another Florida Republican eying a presidential run.

"If Jeb's last name was Brown instead of Bush, I think he would be the front-runner today," said former Mississippi Gov. Haley Barbour, who says Bush has the record, poise and skill.

"How much Bush fatigue is there today compared with two years ago?" he asked. "How much is there today compared with two years from now?"

Hillary Rodham Clinton, the likely Democratic front-runner in 2016, faces a similar issue, but enthusiasm among her base is higher and she can make a historical argument if she tries to become the first female president.

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Not long ago, Bush suggested his time had passed. "There's a window of opportunity in life, and for all sorts of reasons this was probably my time," he said in a 2012 interview. "I'm not sure I would have been successful as a candidate either. These are different times than just six years ago, when I last ran, or even longer than that."

But if Bush seems out of step in the Ted Cruz era, it also could be an advantage, backers say, with voters looking for someone to rise above the fighting.

"The Republican Party is going through a complete move to the center, rejecting the far right, and he embodies that," said Tom McInerney, a Wall Street investor and GOP donor who saw Bush in New York. "He's not extreme. He's thoughtful, he's intelligent. He's electable, and most of the others are not."

Bush's camp has kept him from reporters, saying he's not interested in the speculation of a campaign. But he continues to stoke the talk. On Thursday, Bush will host a Miami fundraiser for Gov. Terry Branstad of Iowa, home to the country's first nominating contest.

And speeches like the impassioned one he gave in New York show some fire in the belly.

"The American Dream is slowly being replaced by something economists call 'stickiness at the ends,' " Bush told New York's top political donors. "Those born wealthy will stay there, and those who are poor will do the same. And those in the middle, the group that has defined who we are as a nation for two centuries, are shrinking and they are feeling the squeeze. Today for the first time over the longest period of time, a majority of Americans believe that their children will have less opportunity than what they had. If our people are not rising, our nation will not rise."

He continued the thought at the college graduation on Saturday: "This is where the next generation of American leaders have a huge role to play."

Alex Leary can be reached at leary@tampabay.com. Follow him on Twitter @learyreports.